Why do I get different Denoising Normal Information when exporting as HDR and EXR files?
This may very well be a bug, but even if it were not, HDR and PNG are poor choices here.

HDR is a horribly inefficient format when compared to EXR. This is doubly so when considering that an albedo represents a range of energy reflectance of a whole. That is, the primary value range for an albedo is 0% to 100%, or in normalized float terms, typically 0.0 to 1.0.

So why is HDR horrifically inefficient? The encoding scheme is dedicated to encoding much larger ranges. That trade off means fewer bits are allocated for that crucial range of values between 0.0 and 1.0. The same applies to scene radiometry as well, where the emission range frequently isn’t using up the entire bit range of HDR’s encoding scheme.

EXR is by far and above the only file format one should be using when dealing with these sorts of things. Sadly, some people are forced into other file encodings due to poor software, and have to make do with awful encodings.

This link is extremely informative for those who seek further information on the file encoding quantisations:

http://www.anyhere.com/gward/hdrenc/hdr_encodings.html